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Truth, Proof and Infinity

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Cover of 'Truth, Proof and Infinity'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Introduction and Statement of the Problem
  3. Altmetric Badge
    Chapter 2 What’s Wrong with Set Theory?
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    Chapter 3 What’s Wrong with Infinite Quantifiers?
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    Chapter 4 Abstraction and Idealisation
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    Chapter 5 What are Constructions?
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    Chapter 6 Truth and Proof of Logical Formulae
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    Chapter 7 The Need for a Theory of Constructions
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    Chapter 8 Theories of Constructions
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    Chapter 9 Hilbert’s Formalism
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    Chapter 10 Open-Endedness
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    Chapter 11 Analysis
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    Chapter 12 Introduction to Part II
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    Chapter 13 Design of the Term Language
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    Chapter 14 The Term Language
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    Chapter 15 From the Term Language to the Expanded Term Language
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    Chapter 16 The Expanded Term Language
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    Chapter 17 The Protological Sequent Calculus
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    Chapter 18 Commentary on the Protological Axioms and Rules
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    Chapter 19 From Protologic to Expanded Protologic
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    Chapter 20 Expanded Protologic
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    Chapter 21 From Expanded Protologic to the Coding of Trees
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    Chapter 22 The Coding of Trees
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    Chapter 23 The Expanded Term Language as a Functional Programming Language
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    Chapter 24 Introduction to Part III
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    Chapter 25 From the Coding of Trees to Logic
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    Chapter 26 Logic
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    Chapter 27 From Logic to the Calculus of Proof Functions
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    Chapter 28 Calculus of Proof Functions
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    Chapter 29 From Calculus of Proof Functions to the Logic of Partial Terms
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    Chapter 30 Logic of Partial Terms
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    Chapter 31 From Logic of Partial Terms to Heyting Arithmetic
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    Chapter 32 Heyting Arithmetic
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    Chapter 33 From Heyting Arithmetic to Peano Arithmetic
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    Chapter 34 Peano Arithmetic
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    Chapter 35 Conclusions on Arithmetic
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    Chapter 36 Introduction to Part IV
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    Chapter 37 From Expanded Protologic to the Second-Order Coding of Trees
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    Chapter 38 The Second-Order Coding of Trees
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    Chapter 39 From the Second-Order Coding of Trees to Second-Order Logic
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    Chapter 40 Second-Order Logic
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    Chapter 41 From Second-Order Logic to Second-Order Calculus of Proof Functions
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    Chapter 42 Second-Order Calculus of Proof Functions
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    Chapter 43 From Second-Order Calculus of Proof Functions to Second-Order Logic of Partial Terms
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    Chapter 44 Second-Order Logic of Partial Terms
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    Chapter 45 From Second-Order Logic of Partial Terms to Second-Order Heyting Arithmetic
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    Chapter 46 Second-Order Heyting Arithmetic
  48. Altmetric Badge
    Chapter 47 From Second-Order Heyting Arithmetic to Second-Order Peano Arithmetic
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    Chapter 48 Second-Order Peano Arithmetic
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    Chapter 49 Conclusions on Analysis
Attention for Chapter 47: From Second-Order Heyting Arithmetic to Second-Order Peano Arithmetic
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Chapter title
From Second-Order Heyting Arithmetic to Second-Order Peano Arithmetic
Chapter number 47
Book title
Truth, Proof and Infinity
Published by
Springer, Dordrecht, January 1998
DOI 10.1007/978-94-017-3616-9_47
Book ISBNs
978-9-04-815105-9, 978-9-40-173616-9
Authors

Peter Fletcher